Days 1 - 10

Sanderson M. Smith

STATISTICS/FINANCE ASSIGNMENTS

TEXT: The Practice of Statistics, by Yates, Moore, Starnes.

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Day #1 (STATISTICS):

 "There are two kinds of statistics: The kind you look up and the kind you make up." -Rex Stout

Emphasis on graphical displays and numerical summaries of data distributions: Box-whisker plots and the big five summary [Minimum, 25th percentile (Q1), Median, 75th percentile (Q3), Maximum].

ASSIGNMENT: In TEXT, read pages 42-46. Do Exercise 1.36 (abc) on page 47.

Example emphasizing terminology: Consider the following data set:

 4 6 7 7 8 10 15 16 20 23 100

Number of scores = N = 11.
Big five summary: Min = 4, Q1 = 7, Median = 10, Q3 = 20, Max = 100.
Mean = 19.64
Range = 100 - 4 = 96.
Interquartile range (IQR) = 20 - 7 = 13.
Mode = 7.

Mean, median and mode are measures of center.
Range and IQR are measures of spread.
The extreme score of 100 (an outlier) considerably influences the mean, but does not influence the median.

Class activity: Collecting and analyzing data for dice game scores. (Handout). Basic rules: Two dice are rolled. Each player assume TOTAL as initial score. Players who wish to keep TOTAL as session score sit down. For those remaining in session, dice rolled again. If TOTAL is 2, 11, or 12, standing players assume a score of 0 for the session. Otherwise TOTAL is added to previous score. Continue process. Session ends when all players are seated. A game consists of three sessions. A player's score is the total of the scores for the three sessions.

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Day #2 (STATISTICS):

 "Numbers are like people; torture them enough and they'll tell you anything." -Frederick Mosteller

Emphasis on graphical displays and numerical summaries of data distributions: Box-whisker plots and the big five summary [Minimum, 25th percentile (Q1), Median, 75th percentile (Q3), Maximum]. Also... Dotplots, bar charts, and histograms.

ASSIGNMENT: In TEXT, read pages 8-12, 18-22. For the Jurassic Park section you read (CONTROL, SEARCH, or RETURN) prepare graphical displays of word length similar to those done in the class activity. You should prepare a box-whisker plot, a frequency histogram, and a relative frequency histogram for word lengths. Prepare a bar chart to display the four word length categories (small, medium, big, very big).

Class Activity: Here is a reading section from Jurassic Park.

 "But you don't get this graph," Malcolm said. "The graph you actually got is a graph of a breeding population. Your compys are breeding." Wu shook his head. "I don't see how." "They're breeding, and so are the othnielia, the Maiasaurs, the hypsys...and the velociraptors." "Christ," Muldoon said. "There are raptors free in the park."

 #Letters Frequency.......................................... Categories of Words Frequency 1 . SMALL (1-3 letters) . 2 . MEDIUM (4-6 letters) . 3 . BIG (7-9 letters) . 4 . VERY BIG (10 or more) . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 .

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Day #3 (STATISTICS):

 "Any teacher who can be replaced by technology should be." -Arthur C. Clarke

ASSIGNMENT: In TEXT, read pages 25-26. Be familiar with the phrases symmetric, skewed right, and skewed left. Also, read the SUMMARY on pages 33-34. Complete the worksheet provided in class that contained this table of quiz scores.

 Score 0 1 2 3 4 5 6 7 8 9 10 Freq. 3 0 0 12 39 29 18 32 20 7 0

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Day #4 (STATISTICS):

 "A statistician is a man who comes to the rescue of figures that cannot lie for themselves." -Abraham Maslow

ASSIGNMENT: In TEXT, read pages 11-15. Be familiar with the phrases symmetric, skewed right, and skewed left. Make a good stemplot for the data displayed in problem 1.10 (page 17). Make a split-leaf stemplot for the presidential ages in Table 1.4 on page 19.

Class activity will involve examining the data for Michigan college tuitions as they appear in the stemplot on page 18. Also, creation of stemplots of this data set.

 87 45 66 67 90 98 62 44 87 69 95 92 74 81 77 58 87 85 83 72

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Day #5 (STATISTICS):

 "A mind that is stretched by a new experience can never go back to its old dimensions." -Oliver Wendell Holmes
Class time was used to introduce spreadsheet and spreadsheet manipulations. As an assignment, students were instructed to activate Excel on their respective computers and "fiddle around" with the concepts introduced during the class period.

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Day #6 (STATISTICS):

 "78% of all statistics are made up on the spot." -H. G. Wells
(Same as previous assignment). Class time was used to introduce spreadsheet and spreadsheet manipulations. As an assignment, students were instructed to activate Excel on their respective computers and "fiddle around" with the concepts introduced during the class period.

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Day #7 (STATISTICS):

 "To be a statistician is great! You never have to be 'absolutely sure' of something...being 'reasonably certain' is enough." -Pavel Guarisma
In text, read pages 18-24 (histograms).

The data provided in exercise 1.12 (page 23) is provided to you. Enter the fifty pieces of data into your calculator and do the following:

1. Calculate mean, min., Q1, median, Q3, max., range, IQR.

2. Construct a boxplot to display the data. Identify outliers.

3. Construct the following histograms to display the data:

a) histogram with class interval length = 2.
b) historgram with class interval length = 4.
c) histogram with class interval length = 5.
d) histogram with class interval length = 10.

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Day #8 (STATISTICS):

 "You know how dumb the average guy is? Well, by definition, half of them are even dumber than that. " -J. R. "Bob" Dobbs
In text, read pages 49-52 (up to exercises). Using the data sheet supplied in class, respond to the requests on the sheet. (Basically, assignment requires construction of back-to-back stemplots, parallel boxplots, and histograms.

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Day #9:

 "Facts are such horrid things." -A character in Jan Austen's Lady Susan
Worksheet provided in class. Assignment involves empirical results from rolling three dice. Show the distribution of the random variable x, where x is the sum of the up faces on the three dice. Possible values of x are 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18. For the data set obtained, calculate the mean and standard deviation. Also construct a boxplot to display the obtained data.

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Day #10:

 "A knowledge of statistics is like a knowledge of" foreign language or of algebra; it may prove of use at any time under any circumstances." -Arthur L. Bowley
(Day 12)

(1) Complete the standard deviation/variance worksheet provided in class.

(2) Complete your analysis of this situation: A company has 20 employees, including 6 minorities. After a productive year the company decides to award each of 5 randomly selected employees a bonus of \$5,000 each. The company does the selection process and it turns out there are no minorities among the selected five. There is suspicion that perhaps discrimination was involved in the selection process. That is, the randomness of the process is being questioned. STATISTICALLY SPEAKING, IS THERE SIGNIFICANT EVIDENCE TO SUGGEST THAT THE SELECTION PROCESS WAS NOT RANDOM.